Timeline for Reference request: a locally cyclic group is isomorphic to a section of the rational numbers
Current License: CC BY-SA 3.0
6 events
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| Oct 4, 2011 at 17:40 | comment | added | user6976 | @Mark: The proof should go like this. First embed your Abelian group into a full group. Note that the full group can be assumed locally cyclic too. Then use the description of Abelian full groups. | |
| Oct 4, 2011 at 17:20 | comment | added | Mark Wildon | Many thanks for these references. For torsion-free groups the result is mentioned on page 109 of Fuchs "Infinite Abelian Groups", Volume II. I cannot find the torsion case in Fuchs in any explicit form. Marshall Hall's "Theory of Groups" page 340 has "The additive group of rationals $R_+$ is a locally cyclic group which is aperiodic, and the group $R_+$ modulo $1$ is a periodic locally cyclic group. It is not too difficult to show that a locally cyclic group is a subgroup of one of these two groups." (No proof is given.) | |
| Oct 2, 2011 at 16:54 | vote | accept | Mark Wildon | ||
| Sep 30, 2011 at 17:07 | history | edited | user6976 | CC BY-SA 3.0 |
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| Sep 30, 2011 at 14:06 | history | edited | user6976 | CC BY-SA 3.0 |
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| Sep 30, 2011 at 13:44 | history | answered | user6976 | CC BY-SA 3.0 |